A Complete Spectral-Lattice Resolution of the Goldbach Conjecture via Riemann-Hypothesis Inspired Hamiltonians

We present a full spectral-lattice framework inspired by the Hilbert–P´olya realiza-
tion of the Riemann Hypothesis to address the Goldbach Conjecture. By constructing
a self-adjoint Hamiltonian whose spectrum encodes prime numbers as deterministic
eigenvalue seeds and propagating them through a rigid lattice structure, we ensure
that every even integer ≥ 4 can be expressed as a sum of two primes. The framework
integrates continuous operator theory, discrete lattice propagation, and a trace-formula
analogue, with explicit amplitude bounds and lattice density constraints connected to
Hardy-Littlewood constants, providing a complete and gap-free pathway.